Collisionless shock acceleration of quasimonoenergetic ions in ultrarelativistic regime

Collisionless shock acceleration of carbon ions $\left({\mathrm{C}}^{6+}\right)$ is investigated in the ultrarelativistic regime of laser-plasma interaction by accounting for the radiation reaction force and the pair production in particle-in-cell simulations. Both radiation reaction force and pair-plasma formation tend to slow down the shock velocity, reducing the energy of the accelerated ions, albeit extending the timescales of the acceleration process. The slab plasma target achieves a lower energy spread while the target with a tailored density profile yields higher ion acceleration energies.

Figure 1

Number density of plasma normalized by the initial density at different instants. First, second, and third columns represent the cases of no RR [panels (a), (d), and (g)], with RR [panels (b), (e), and (h)], and with RR+PP [panels (c), (f), and (i)], respectively. The shock density jump, $n_{\mathrm{sh}}$ (second vertical axes), averaged in the $y$ direction is overplotted with a black dotted line in each case.

Figure 2

Densities of pairs [panels (a) and (c), normalized by $n_c]$ and the photons [panels (b) and (d), normalized by initial electron density, $300n_c]$ generated at different times (top row 240 fs and bottom row 390 fs) corresponding to the last column in Fig. 1. The peak pair density (black) is overplotted in panels (a) and (c). The peak value reaches up to $\sim 5n_c$ (second vertical axes) around the laser plasma interface at 390 fs [marked by an arrow in panel (c)].

Figure 3

Fraction of average laser energy ${\mathcal{E}}_L$ being converted to each species “$s$” ($\mathrm{\Delta }{\eta }_s={\mathcal{E}}_s/{\mathcal{E}}_L$) in logarithmic scale [top panel (a)]. The BW electrons [green line in panel (a)] are distinguished from the plasma electrons [red line in panel (a)]. Average kinetic energy ($y$-averaged) for each species at $t=240$ fs [panels (b) and (c)]. The electron and ion energies are shown in panel (b), while the pairs and photons are shown in panel (c).

Figure 4

Angular distribution of photons [panel (a)] and pairs [panel (b)] at 390 fs.

Figure 5

$\left(x\text{−}t\right)$ plot of ion density (normalized by initial density) indicating shock and piston velocities in the three cases considered [(a) corresponds to the no RR case, (b) corresponds to RR, and (c) corresponds to the RR+PP case].

Figure 6

Development of $y$-averaged electrostatic field energy densities due to $E_x$ [in panels (a) and (c)] and due to $B_z$ [in panels (b) and (d)] normalized by ${\epsilon }_{E_L}=(1/8\pi )E_L^2$ at $t=240$ fs (top row) and 390 fs (bottom row). The shock front is marked by arrows of respective colors, whereas the position of the laser piston is marked by the circular marker. The insets at the top of panels (a) and (c) show the TNSA field at the end of the target.

Figure 7

Ion energy spectrum at $t=390$ fs in panel (a) and 570 fs in panel (b). Here $F_{C^{6+}}\left(E\right)$ is the energy distribution function of carbon ions. The case without the radiation reaction force (black line) has a peak energy of 321 MeV with an energy spread of $\sim 3\%$ while for the other two cases (RR and RR+PP) it is 188 and 170 MeV, respectively, with similar energy spreads $\sim 2\%–3\%$. At a later time of 570 fs in panel (b) it can be seen that the ions gain more energy (928 MeV with $\sim 2.6\%$ spread, 495 MeV with $\sim 2.8\%$ spread, and 465 MeV with $\sim 1.7\%$ spread, respectively).

Figure 8

Electron phase space [in panels (a), (c), and (e)] and ion phase space [in panels (b), (d), and (f)] at $t=390$ fs for all three cases [panels (a) and (b) correspond to the no RR case, panels (c) and (d) correspond to the RR case, and panels (e) and (f) correspond to the RR+PP case].

Figure 9

Number density of plasma normalized by the initial peak plasma density at different instants. First, second, and third columns represent the cases of no RR [panels (a), (d), and (g)], with RR [panels (b), (e), and (h)], and with RR+PP [panels (c), (f), and (i)], respectively. The shock density jump, averaged in the $y$ direction, is overplotted (second $y$ axis) with a black dotted line in each case.

Figure 10

$\left(x\text{−}t\right)$ plot of the ion density indicating shock and piston velocities in the three cases considered [no RR case in panel (a), RR case in panel (b), and RR+PP case in panel (c)]. Also overplotted is the shock density jump, $n_{\text{sh}}$, that clearly demarcates the CSA dominated regime from the hybrid regime (CSA+RPA).

Figure 11

Electron phase space (left column) and ion phase space (right column) at $t=480$ fs for all three cases [panels (a) and (b) correspond to the no RR case, panels (c) and (d) correspond to the RR case, and panels (e) and (f) correspond to the RR+PP case].

Figure 12

Ion energy spectrum at $t=480$ fs in panel (a). Here $F_{{\text{C}}^{6+}}\left(E\right)$ is the energy distribution function of carbon ions. The case without the radiation reaction force (black line) has a peak energy of 900 MeV with an energy spread of $\sim 20\%$ while for the case with RR and RR+PP it is 551 MeV with a spread of $\sim 25\%$ and 548 MeV with the same spread. At a later time $t=630$ fs in panel (b), the energies gained are much higher for each case, but the energy spread broadens, viz., 1.302 GeV ($\sim 28\%$), 1.432 GeV ($\sim 47\%$), and 1.382 GeV ($46\%$).